Another departure and I hope a useful metaphor when looking at the impact of “Value of Time” calculations used in transport appraisal!
A long time ago, I studied Physics in Manchester, and first encountered the non-intuitive nature of Quantum Physics. I didn’t really understand it then, read some books after University and thought I did…but didn’t. In fact, the whole subject is perhaps best described by Nobel Laureate, Richard Feynmann, who is purported to have said, “If you think you understand quantum mechanics, you don’t understand quantum mechanics”.
It really runs counter to our common sense understanding of the world. Anyone who has grappled with the implications of the double slit experiment, non-locality and spooky action at a distance, will concur and that’s before we get to Schrodinger’s dead and alive cat. Yet the mathematics wrapped around Quantum Physics provides us the most accurate tool to understand a sub-atomic world that would otherwise remain hidden from human exploration.
Many have tried to apply some of the implications of Quantum Physics to new age interpretations of the world…most of which I view as woo. Despite that, l’d like to use one aspect of Quantum physics as a metaphor for an issue impacting transport planning and especially the treatment of the “value of time”.
First, I want to focus on the Photoelectric effect; and the theory set out by Einstein in the years that followed Planck’s[i] (the originator of Quantum theory) bombshell revelation that electromagnetic energy could be emitted only in quantised form. Simply put electromagnetic energy can only be a multiple of an elementary unit (later called photons) where the energy E = hv where h is Planck’s constant and ν is the frequency of the radiation.
This insight also had to complement the clear evidence of the wave like characteristics of electromagnetic radiation and so manifest the essential wave/particle duality of EM radiation which is a key feature of Quantum physics.
This then brings us to Einstein’s[ii] insight into the photoelectric effect[iii]. The photoelectric effect is the emission of electrons when electromagnetic radiation, such as light, hits a material. Electrons emitted in this manner are called photoelectrons.
The revelation Einstein introduced was that the ability of incoming light to generate photoelectrons (so a current) from a suitable material depends, not on the number of photons (so the intensity of the light), but of the frequency of that light and so the energy of individual “particles” of light. That energy had to be of a sufficient level to “dislodge” an electron from the material. No matter how many photons (or intensity or their aggregate energy) no photoelectric effect will be observed until the frequency and so the energy per “photon” reaches a certain level. Einstein also observed, building on Planck’s insight that the emissions of such electrons were quantised and not on a spectrum
Now lets look at Transport Planning and the value of Time[iv]. Very roughly, when transport planners are estimating the transport user benefits of a transport intervention, they normally multiply the journey time savings by a “value of Time” (VoT) metric. There are different values to be used in different circumstance, and transport models do accommodate different elasticities of demand in some circumstances. However, we are sometimes left with really counter intuitive outputs form VoT calculations. For example, the WG were recently obliged to assess (using HMT Green book guidelines) the economic impact of the 20mph limits now in place in Wales.
Over 60 years that formally produced a disbenefit of over £4Bn[v] based on the following table
One can see that the total impact is made up by aggregating 000s of very small changes, over 60 years, of less than two minutes to journey times. The question is, in the real world, is the calculation and output value in any sense “real”. In most circumstance, I think not .
For me this is like 000s of photons whose frequency is not sufficient to generate an electron via the photoelectric effect. I assert that a small change to a big number generally does not in fact have any meaningful impact on people’s choices. There ought to be a threshold (absolute and as a proportion) above which the impact of the change in journey time does have an impact – but below it does not?
Look at this, what is in aggregate the biggest impact?
10 people being able to go 20 minutes faster on a journey that used to take 60 mins (a 33% reduction in journey time!) – so 10*20mins = 200Min
OR
100 people able to go 2 mins faster on a 60-minute journey (3.3% journey time saving) – again so 100 *2 ins = 200mins.
I assert that whilst the maths gives the same number, it is only the first example that has a meaningful impact on people’s choices. And it does not matter how many people save 2 minutes on a one hour trip (there could be 10,000 people) there is still no impact.
This is a common criticism of transport planning and appraisal where big numbers are often generated like this, by aggregating thousands or even millions of small incremental values over years and even decades. (This is how most roads schemes were approved!)
So, like the photo electric effect, we need to perhaps modify out approach and recognise the “quantum” effect and the minimum required “change” in journey time sufficient to actually have an impact on people’s choices and behaviour. Now I don’t know what that “value” is or should be. However, without this factor, we have used (in my view) a flawed methodology that has resulted in us building 000s of miles of roads and degrading our public transport (let alone failing to capture and quantify the many wider benefits of public transport use!).
I think this is the Value of Time catastrophe – something physicists will understand[vi]!
As a final point we need to remember that Quantum physics is based on statistical probabilities that can be (very) accurately modelled. In contrast, economics and transport planning are based on much more unpredictable human behaviours; yet we use transport models and supply & demand curves as if they were also describing underlying and predictable features of a physical science!
We need to be careful that decisions on major public investment are not overly swayed by mathematical interpretations and presentation thereof, that in some circumstances, have no real-world merit.
[i] Max Planck – Biographical – NobelPrize.org
[ii] The Nobel Prize in Physics 1921 – NobelPrize.org
[iii] Photoelectric Effect – an overview | ScienceDirect Topics
[iv] Values of travel time savings and reliability: final reports – GOV.UK (www.gov.uk)
[v] Senedd, Explanatory Memorandum to the Restricted Roads (20 mph Speed Limit) (Wales) Order 2022 EM template for sub leg (senedd.wales)
[vi] Black Body Radiation – an overview | ScienceDirect Topics
Mark Barry 